Universal gravitation 4-determine the weight of astronaut on planet Z

An astronaut weighs 833N on the surface of the Earth. Determine the weight of the astronaut on Planet Z if the planet's mass is 50.0 times the mass of the Earth and has a radius of 10.0 times the radius of the Earth.

2. Relevant equations

Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3

motion of planets must conform to circular motion equation: Fc=4∏2mR/T2

From Kepler's 3rd law: R3/T2=K or T2=R3/K

Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2

Newton's Universal Law of Gravitation: F=Gm1m2/d2

value of universal gravitation constant is: G=6.67x10-11N*m2/kg2

weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2

g=Gme/(Re)2

determine the mass of the Earth: me=g(Re)2/G

speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h

period of the Earth-orbiting satellite: T=2∏√R3/GMe

Field strength in units N/kg: g=F/m

Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp[Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3

motion of planets must conform to circular motion equation: Fc=4∏2mR/T2

From Kepler's 3rd law: R3/T2=K or T2=R3/K

Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2

Newton's Universal Law of Gravitation: F=Gm1m2/d2

value of universal gravitation constant is: G=6.67x10-11N*m2/kg2

weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2

g=Gme/(Re)2

determine the mass of the Earth: me=g(Re)2/G

speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h

period of the Earth-orbiting satellite: T=2∏√R3/GMe

Field strength in units N/kg: g=F/m

Determine mass of planet SUP]2[/SUP]

3. The attempt at a solution

Fg=weight=833N on surface of the Earth

mp=50 * (5.98*1026 kg)
Rp=10*(6.38*106m)= 6380000 m

I used gp=GMp/(Rp)2=489.95 N/kg

I also used Fg=gxmo and manipulated the equation to solve for mo=1.7 kg

Just wondering if someone would be able to have a look at my attempt and let me know if its wrong and if it is maybe point out where it is that I made my mistake. It would be greatly appreciated! Thanks again so much in advance!

A lot of the relevent equations that you posted are actually totally irrelevant. In fact, Newton's universal law of gravitation is all you need, and a couple of the other equations you have there are just Newton's universal law of gravitation applied to specific situations.

For me, step 1 would be to find the mass of the astronaut. It is certainly not 1.7 kg! Think about that for a second. How can a human being have a mass of only 1.7 kg?

Getting the mass shouldn't be too hard, since you know the weight on Earth, and you know g on Earth.

Then the second step, once you have the mass, would be to multiply it by the gp value that you computed to get the weight on the planet.

EDIT: Er, yeah, or you could do what Doc Al said, which is even smarter.

Staff: Mentor

do I multiply the gp with the mass of the astronaut on earth in order to find out the value of his mass on the planet Z?

You can certainly do it that way. The mass is the same everywhere, of course. But you'll have to redo your calculation of gp. You can do that easily by just comparing the calculation to that of ge. (Again, hardly any calculation needed. But more than if you followed my original method.)

The question asked for weight, not mass. Weight and mass are two different things in physics, even though in everyday language they are often used interchangeably. You just need to use the physics definition of mass and weight.

Staff: Mentor

so is it just g of the planet which I found to be 489.95N/kg, and times that by 85kg (which is the mass of the astronaut)? If I do that I get weight=force due to gravity=41646.12N

As I said earlier, you'll need to redo your calculation of g on the planet as it is incorrect. But once you have the correct value of g, then you can multiply it by the mass to find the weight on the planet. (That's the hard way, but perfectly OK.)

Staff: Mentor

Just for fun, try the easy way. Answer this: If the mass of the planet is increased by a factor of 50, what would happen to the weight of the astronaut? Would it go up or down? By what factor? (Imagine everything else is held fixed.)

Note that this is equivalent to asking: If the mass of the planet is increased by a factor of 50, what would happen to the value of g at the surface?